NEED HELP, 1) 4x^2−2x(3x+1)=5 2) −5x(x+6)=4(x−3)−10 3) x^2+(1−x)(1−3x)=x 4) (x−8)(2x+3)=(3x−5)(x+4)

I would really appreciate a brainliest for this, it took me quite a while : )

1.) imaginary; x ∉ R

2.)

3.)

4.)

Step-by-step explanation:

1.) 4x² - 2x(3x + 1) = 5

Distribute.

4x² - 6x² + 2x = 5

Combine like terms, change the signs.

-2x² + 2x = 5 ⇒ -2x² + 2x - 5 = 0

Insert into the quadratic formula.

; a = -2; b = 2; c = -5

Plug in values for a, b, & c.

Multiply and add/subtract.

⇒

The is imaginary, therefore x ∉ R

2.) -5x(x + 6) = 4(x - 3) - 10

Distribute, combine like terms.

-5x² - 30x = 4x - 22

Change the signs.

5x² + 34x - 22 = 0; a = 5; b = 34; c = -22

Plug in values for a, b, & c in the quadratic formula.

Multiply and add/subtract, simplify.

3.) x² + (1 - x)(1 - 3x) = x

Multiply, combine like terms.

x² + 1 - 3x - x + 3x² = x ⇒ 4x² - 4x + 1 = x

Change the signs.

4x² - 5x + 1 = 0; a = 4; b = -5; c = 1

Insert a, b, & c into quadratic formula.

Multiply, add, subtract, simplify.

4. (x - 8)(2x + 3) = (3x - 5)(x + 4)

Multiply, combine like terms.

2x² + 3x - 16x - 24 = 3x² + 12x - 5x - 20 ⇒ 2x² - 13x -24 = 3x² + 7x - 20

Change the signs.

x² + 20x + 4 = 0; a = 1; b = 20; c = 4

Insert a, b, & c into quadratic formula.

Multiply, add, subtract, simplify.

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a